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# FP3 - 2 Limits Questions - Stuck

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Q1:

I have tried multiplying top and bottom by and that didn;t get me anywhere, I then tried expanding the ex's and after some working eventually got stuck at

I have been on it for a while so a solution would be better than a hint, unless there is something small that I am missing or a mistake somewhere.

Q2:

For this one I expanded ex and brought the (1-x) to the top and expanded it, multiplied it out and I am stuck at

Same as above, all help is appreciated.

Thnx
2. On Q1 you could try multiplying top and bottom by e^-x.
3. (Original post by ian.slater)
On Q1 you could try multiplying top and bottom by e^-x.
Yea, that works lol. The answer is -1, why didn't I see something so simple !!
4. (Original post by member910132)

Q1:

I have tried multiplying top and bottom by and that didn;t get me anywhere, I then tried expanding the ex's and after some working eventually got stuck at

I have been on it for a while so a solution would be better than a hint, unless there is something small that I am missing or a mistake somewhere.

Q2:

For this one I expanded ex and brought the (1-x) to the top and expanded it, multiplied it out and I am stuck at

Same as above, all help is appreciated.

Thnx
second one:
large +ve x makes e^x +ve and 1-x -ve so F is -ve. Now consider the relative order of exponentials and linear expressions in x.
5. (Original post by ian.slater)
On Q1 you could try multiplying top and bottom by e^-x.
Just tried that for Q2 and I get:

Using the general result that xe^(-x) tends to 0 as x tends to infinity my only problem is showing how F(x) goes to negative infinity and not just infinity.
6. (Original post by member910132)

Q1:

I have tried multiplying top and bottom by and that didn;t get me anywhere, I then tried expanding the ex's and after some working eventually got stuck at

I have been on it for a while so a solution would be better than a hint, unless there is something small that I am missing or a mistake somewhere.

Q2:

For this one I expanded ex and brought the (1-x) to the top and expanded it, multiplied it out and I am stuck at

Same as above, all help is appreciated.

Thnx
You could use L'Hopital' s Theorem...they both come out very easily then.....
7. (Original post by ben-smith)
second one:
large +ve x makes e^x +ve and 1-x -ve so F is -ve. Now consider the relative order of exponentials and linear expressions in x.
Sorry, I don't follow the second part.
8. (Original post by mikelbird)
You could use L'Hopital' s Theorem...they both come out very easily then.....
That isn't on the AQA FP3 syllabus and I don't want to learn stuff that ain't on the syllabus.
9. (Original post by member910132)
Sorry, I don't follow the second part.
from an intuitive point of view, e^x is like a polynomial of very high degree and so it's going to tend to infinity faster than a linear function.
10. (Original post by member910132)
Just tried that for Q2 and I get:

Using the general result that xe^(-x) tends to 0 as x tends to infinity my only problem is showing how F(x) goes to negative infinity and not just infinity.
x e^-x > e^-x
11. For Q2 I am almost there, I just need to show that will tendo to . as but I need to show that they tend to from the negative as only then will the function .
12. (Original post by mikelbird)
You could use L'Hopital' s Theorem...they both come out very easily then.....
Not allowed.
13. So is it sufficient for me to say that as because both terms in the denominator tend to zero and ?

Edit: So can it be said that as and hence ?
14. Bump - will anyone verify my above post so I can finish this thread ?
15. (Original post by member910132)
Bump - will anyone verify my above post so I can finish this thread ?
I'd be happy with it.

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